Induced Gravity II: Grand Unification

As an illustration of a renormalizable, asymptotically-free model of induced gravity, we consider an $SO(10)$ gauge theory interacting with a real scalar multiplet in the adjoint representation. We show that dimensional transmutation can occur, spontaneously breaking $SO(10)$ to $SU(5){\otimes}U(1),$ while inducing the Planck mass and a positive cosmological constant, all proportional to the same scale $v$. All mass ratios are functions of the values of coupling constants at that scale. Below this scale (at which the Big Bang may occur), the model takes the usual form of Einstein-Hilbert gravity in de Sitter space plus calculable corrections. We show that there exist regions of parameter space in which the breaking results in a local minimum of the effective action, and a {\bf positive} dilaton $(\hbox{mass})^2$ from two-loop corrections associated with the conformal anomaly. Furthermore, unlike the singlet case we considered previously, some minima lie within the basin of attraction of the ultraviolet fixed point. Moreover, the asymptotic behavior of the coupling constants also lie within the range of convergence of the Euclidean path integral, so there is hope that there will be candidates for sensible vacua. Although open questions remain concerning unitarity of all such renormalizable models of gravity, it is not obvious that, in curved backgrounds such as those considered here, unitarity is violated. In any case, any violation that may remain will be suppressed by inverse powers of the reduced Planck mass.Comment: 44 pages, 5 figures, 2 tables. v2 has new discussion concerning stability of SSB plus related appendix. Additional references added. v3 is version to be published; contains minor revision

Zero modes in de Sitter background

There are five well-known zero modes among the fluctuations of the metric of de~Sitter (dS) spacetime. For Euclidean signature, they can be associated with certain spherical harmonics on the $S^4$ sphere, viz., the vector representation $\bf5$ of the global $SO(5)$ isometry. They appear, for example, in the perturbative calculation of the on-shell effective action of dS space, as well as in models containing matter fields. These modes are shown to be associated with collective modes of $S^4$ corresponding to certain coherent fluctuations. When dS space is embedded in flat five dimensions $E^5,$ they may be seen as a legacy of translation of the center of the $S^4$ sphere. Rigid translations of the $S^4$-sphere on $E^5$ leave the classical action invariant but are unobservable displacements from the point of view of gravitational dynamics on $S^4.$ Thus, unlike similar moduli, the center of the sphere is not promoted to a dynamical degree of freedom. As a result, these zero modes do not signify the possibility of physically realizable fluctuations or flat directions for the metric of dS space. They are not associated with Killing vectors on $S^4$ but can be with certain non-isometric, conformal Killing forms that locally correspond to a rescaling of the volume element $dV_4.$ For convenience, we frame our discussion in the context of renormalizable gravity, but the conclusions apply equally to the corresponding zero modes in Einstein gravity. We expect that these zero modes will be present to all orders in perturbation theory. They will occur for Lorentzian signature as well, so long as the hyperboloid $H^4$ is locally stable, but there remain certain infrared issues that need to be clarified. We conjecture that they will appear in any gravitational theory having dS background as a locally stable solution of the effective action, regardless of whether additional matter is included.Comment: v4, 28pages, no figures; final journal form, minor changes in text and refs from v

Beyond the Horizon

Cosmic horizons arise in general relativity in the context of black holes and in certain cosmologies. Classically, regions beyond a horizon are inaccessible to causal observers. However, quantum mechanical correlations may exist across horizons that may influence local observations. For the case of de Sitter space, we show how a single particle excitation behind the horizon changes the density matrix governing local observables. As compared to the vacuum state, we calculate the change in the average energy and entropy per unit volume. This illustrates what may be a generic property allowing some features of spacetime beyond a horizon to be inferred.Comment: 9 pages, 1 figur

Structure formation in sugar containing pectin gels – Influence of tartaric acid content (pH) and cooling rate on the gelation of high-methoxylated pectin

The aim of the study was the application of a recently published method, using structuring parameters calculated from dG′/dt, for the characterisation of the pectin sugar acid gelation process. The influence of cooling rate and pH on structure formation of HM pectin gels containing 65 wt.% sucrose were investigated. The results show that the structure formation process as well as the properties of the final gels strongly depended on both parameters. With increasing cooling rates from 0.5 to 1.0 K/min the initial structuring temperature slightly decreased and the maximum structuring velocity increased. The lower the cooling rates, the firmer and more elastic were the final gels. With increasing acid content (decreasing pH from 2.5–2.0) the initial structuring temperatures were nearly constant. The final gel properties varied visibly but not systematically. Gels with the lowest and highest pH were less elastic and weaker compared to those with medium acid concentrations

Treatment of CD30-Expressing Germ Cell Tumors and Sex Cord Stromal Tumors with Brentuximab Vedotin: Identification and Report of Seven Cases

BACKGROUND: Cytotoxic therapy for relapsed and refractory germ cell tumors or metastatic sex cord stromal tumors is rarely effective and is often accompanied by high adverse event rates. Expression of CD30 has been observed in testicular cancers, and patients with CD30-expressing embryonal carcinomas have worse progression-free survival and overall survival than those with CD30-negative tumors. The objective of this study (NCT01461538) was to characterize the antitumor activity of brentuximab vedotin in patients with CD30-expressing nonlymphomatous malignancies. Enrolled patients included seven patients with relapsed or refractory germ cell tumors or metastatic sex cord stromal tumors described in this case series. MATERIALS AND METHODS: Forty patients with relapsed or refractory germ cell tumors, metastatic sex cord stromal tumors, or testicular tumors were screened for CD30 expression; 14 patients had tumors that expressed CD30. Seven patients with CD30-expressing testicular cancer were enrolled in the treatment study: five patients with germ cell tumors, one patient with a Leydig cell tumor, and one patient with a Sertoli cell tumor. Patients were treated with brentuximab vedotin at initial doses of 1.8 or 2.4 mg/kg every 3 weeks. Response assessments were performed at cycles 2 and 4 and every 4 cycles thereafter while the patient was receiving treatment. RESULTS: Two of seven patients achieved an objective response, including one durable complete response and one partial response at a single time point. Both responding patients had germ cell tumors. Treatment with brentuximab vedotin was generally well tolerated. CONCLUSION: Treatment of relapsed or refractory germ cell tumors with brentuximab vedotin can induce durable responses with a manageable toxicity profile. IMPLICATIONS FOR PRACTICE: This case series of seven patients with relapsed or refractory CD30-expressing germ cell tumors (GCTs) or sex cord stromal tumors demonstrates that brentuximab vedotin has activity against GCTs and is well tolerated in heavily pretreated patients with these aggressive tumor types. One patient achieved a complete response that has been durable for almost 4 years since the discontinuation of treatment with brentuximab vedotin. Therefore, brentuximab vedotin may be a valuable option for physicians who care for this difficult-to-treat patient population

Entanglement and Nonunitary Evolution

We consider a collapsing relativistic spherical shell for a free quantum field. Once the center of the wavefunction of the shell passes a certain radius R, the degrees of freedom inside R are traced over. We show that an observer outside this region will determine that the evolution of the system is nonunitary. We argue that this phenomenon is generic to entangled systems, and discuss a possible relation to black hole physics.Comment: 14 pages, 1 figure; Added a clarification regarding the relation with black hole physic